The Mathematics of Diffusion

by Ni, Wei-Ming

• ISBN13: 9781611971965
• ISBN10: 1611971969
• Format: Paperback
• Copyright: 2011-09-26
• Publisher: Society for Industrial & Applied

Summary

Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements and spatial heterogeneity in the classical Lotka–Volterra competition systems. Interspersed throughout the book are many simple, fundamental and important open problems for readers to investigate.

Table of Contents

Preface

Introduction: the heat equation

Dynamics of general reaction-diffusion equations and systems

Qualitative properties of steady states of reaction-diffusion equations and systems

Diffusion in heterogeneous environments: 2 x 2 LotkaâÇôVolterra competition systems

Beyond diffusion: directed movements, taxis, and cross-diffusion

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.